à= at, to, in
de= of, from
Jean écrit la lettre à sa maman-Jean is writing/writes the letter to his mom. It would be a specific letter, THE letter (that was already mentioned in a previous statement) not a general letter that he is writing. This is the usage of the definite article.
Jean écrit une lettre à sa maman= He writes/is writing his mom a letter-a non specific one. This is the usage of the indefinite article.
Jean écrit les lettres à sa maman=Jean is writing/writes the letters to his mom. More than one.
Jean écrit la/une lettre pour sa mère= He's writing the/a letter for her.
As for whether the statement is true or false, that depends on what the goal was. If it was a reading comprehension question, we would need to know the text. If it was a grammatical questions, i.e. was the sentence grammatically correct, we would have to assume no if the sentence did not have the accent and yes if it did.
Questions like these are subjective because we'd need more information to provide the correct response. :-)